Question

A gas present in a container connected to frictionless, weightless piston operating always at one-atmosphere pressure such that it permits the flow of gas outside (with no adding of gas). The graph of n vs T(Kelvin) was plotted & was found to be a straight line with co-ordinates of extreme points as (300, 2) & (200,3). Calculate :

(i) relationship between n & T
(ii) relationship between V & T
(iii) Maxima or minima value of 'V'

• A. $n=\frac{-T}{100}+5,V=\frac{-R{T}^2}{100}+5RT,51.3125l$
• B. $n=\frac{T}{100}-5,V=\frac{-R{T}^2}{100}+5RT,51.3125l$
• C. $n=\frac{-T}{100}+5,V=\frac{-R{T}^2}{100}-5RT,51.3125l$
• D. $n=\frac{-T}{100}-5,V=\frac{R{T}^2}{100}+5RT,51.3125l$

Answer 1

Answer: (A)

$n=\frac{-T}{100}+5,V=\frac{-R{T}^2}{100}+5RT,51.3125l$

(i) Let $n=mT+C$

$2=300m+C$ & $3=200m+C$

On solving $m=-\frac{1}{100},C=5$

So $n=\frac{-T}{100}+5$
(ii) $PV=nRT\Rightarrow 1\times V=(\frac{-T}{100}+5)RT$
$\Rightarrow V=-\frac{R{T}^2}{100}+5RT$

(iii) For max. volume

$\frac{dV}{dT}=0\Rightarrow \frac{-2RT}{100}+5R=0,T=250$

$V=\frac{-R(250{)}^2}{100}+5\times 250R=-625R+1250R$

$V=625R=625\times 0.0821L=51.3125L$

Option A is the answer.